1 5 O ct 1 99 6 Difference Equations and Symmetric Polynomials De - fined by Their Zeros
نویسندگان
چکیده
منابع مشابه
Turán Inequalities and Zeros of Orthogonal Polynomial
We use Turán type inequalities to give new non-asymptotic bounds on the extreme zeros of orthogonal polynomials in terms of the coefficients of their three term recurrence. Most of our results deal with symmetric polynomials satisfying the three term recurrence pk+1 = xpk − ckpk−1, with a nondecreasing sequence {ck}. As a special case they include a non-asymptotic version of Máté, Nevai and Tot...
متن کاملTurán Inequalities and Zeros of Orthogonal Polynomials∗
We use Turán type inequalities to give new non-asymptotic bounds on the extreme zeros of orthogonal polynomials in terms of the coefficients of their three term recurrence. Most of our results deal with symmetric polynomials satisfying the three term recurrence pk+1 = xpk − ckpk−1, with a nondecreasing sequence {ck}. As a special case they include a non-asymptotic version of Máté, Nevai and Tot...
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We study the problem of representing symmetric Boolean functions as symmetric polynomials over Zm. We show an equivalence between such representations and simultaneous communication protocols. Computing a function f on 0 1 inputs with a polynomial of degree d modulo pq is equivalent to a two player simultaneous protocol for computing f where one player is given the first dlogp de digits of the ...
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We introduce a quantization map and study the quantization of Schubert and Grothendieck polynomials, monomials, elementary and complete polynomials. Our construction is based on the quantum Cauchy identity. As a corollary, we prove the Lascoux–Schützenberger type formula for quantum Schubert polynomials of the flag manifold. Our formula gives a simple method for computation of quantum Schubert ...
متن کاملDifference Equations and Symmetric Polynomials Defined by Their Zeros
In this paper, we are starting a systematic analysis of a class of symmetric polynomials which, in full generality,was introduced in [Sa]. The main features of these functions are that they are defined by vanishing conditions and that they are nonhomogeneous. They depend on several parameters, but we are studying mainly a certain subfamily which is indexed by one parameter, r. As a special case...
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